The testing of the experimental drug, recombinant interleukin-2, in patients with HIV infections. There will be two study groups involved in taking different doses of the drug, and one group that will take none of the drug. The study will determine if the use of subcutaneous recombinant IL-2 (proleukin) results in higher CD4 cell counts (count that lowers with HIV virus) in patients infected with HIV, but having a CD4 count of at least 350/mm^3. Normal CD4 count is 1,000-1,500/mm^3. It will also determine if raising the CD4 count will reduce the viral load and lengthen the time until the development of AIDS. The study will also look at two different doses of IL-2 to determine differences in side effects, toxicity stimulation of CD4 counts compliance by the patients. Patients will be recruited from the individual practices of the physicians in the Richmond AIDS Consortium (RAC). Each patient will be randomly assigned to one of the three study groups. Group 1 will receive an injection below the skin of a lower dose of IL-2 for several days, twice a day. Then the patient will have no IL-2 for many weeks. Then another session of IL-2 administration will occur. After a respite of several weeks, a third session will take place. Depending on the results based on the CD4+ count, doses may be continued. Group two will follow the same schedule as group one, but at a higher dose of IL-2. Group three will receive no IL-2. All three groups are encouraged to continue usage of HIV medications while participating in the study. Group 1 and 2 patients are required to take HIV medication, one day before, during, and nine days after the injections of IL-2. During the study, patients will return to the CRC once a month for the first 12 months, and then, every four months until the completion of the study. At monthly visits, 2-3 tablespoons of blood will be drawn for routine and special tests as well as for a future test. There will be questions about health and medications of the patients and a physical exam every four months.